Sectorization is concerned with dividing a large territory into smaller areas, also known as sectors. This process usually simplifies complex problem, leading to easier solution approaches solving the resulting subproblems. Sectors are built several criteria in mind, such equilibrium, compactness, contiguity, and desirability, which vary applications. appears different contexts: sales design, p...

We study a nematic crystal model appearing in [Liu et al.,2007] modeling stretching effects depending on the different shape of microscopic molecules of the material, under periodic boundary conditions. The aim of the present article is twofold: to extend the results given in [Sun & Liu, 2009], to a model with more complete stretching terms and to obtain some stability and asymptotic stability ...